Banach空间中向量优化问题解集的刻画  

Characterization of Solution Sets of Vector Optimization Problems in Banach Spaces

作　　者：李柳芬[1] 

机构地区：[1]四川理工学院理学院

出　　处：《四川理工学院学报（自然科学版）》2012年第6期75-78,共4页Journal of Sichuan University of Science & Engineering(Natural Science Edition)

摘　　要：在有限维空间中,当目标函数凸下半连续时,向量优化问题一定有解,并且解集是紧的。但在无穷维空间中,这不一定成立。不过可以通过在对偶空间中构造一个集合,减弱对目标函数的假设之后,把之前关于有限维空间中向量优化问题的解集的研究,推广到实自反Banach空间中。In finite-dimensional spaces, when the scalar function is convex lower semi-continuity, the efficient solution sets of convex vector optimization problems is nonempty and compact, but in infinite-dimensional spaces this is not estab- lished. However under the structure of a set in dual space and the weakening objective function hypothesis, the results in real finite-dimensional space is extended to real reflexive Banach spaces.

关 键 词：向量优化 弱有效解 0-强制性 回收锥 

分 类 号：O177.2[理学—数学]